A few math problems preferably with a process for solving them .

x square + y square + z square - 2x + 4y - 6z + 14x square - 2x + 1 + y square + 4y + 4 + z square - 6z + 9 (x-1) square + (y + 2) square + (z-3) square.

So: (x-1) squared = 0 (y+2) squared = 0 (z-3) squared = 0x=1 y=2 z=3

x+y+z=6

a to the fourth power - 4a square - 4a - 1

a quadratic + a cubic - a cubic - a square - 3a square - 3a square - 3a - a square (a + 1) - a square (a + 1) - a square (a + 1) - 3a (a + 1) (a + 1) (a cubic - a square - 3a - 1).

a+1) (a cubic + a square - 2a square - 2a square - 2a - a-a-1) (a + 1) [a square (a + 1) - 2a (a + 1) - (a square - 2a - 1)] (a square - 2a - 1).

All 4 problems are solved in the same way: the formula, and I simply write down the equation after the formula.

1: (x - 1)²+y-1 - 1)²+z-2 - 1)²=02: (x-1)²+y+2)²+z-3)²=03:

a -b ) c -d ) 2(ab-cd) =04: original = (a -1) (a +1) -4a (a + 1) (a + 1) (a + 1) (a + 1) (a + 1) (a - a -3a -1) = (a + 1) [a (a -1) - (a + 1) ].

a+1)²(a²-2a-1)

1.Translate to.

That is, to get so, to understand.

42 3 The vertical calculation is as follows:

Divide by the high digit of the dividend, the divisor is 1 digit, and look at the first 1 digit of the dividend.

Because of the difference series an

The yard slides to a2 + a6 = 2a4

a8+a10+a12=3a10

then the original formula = 6 (a4 + a10) = 24

a4+a10=4

then a1 + a13 = 4

So s13=(a1+a13) 13 2=4 13 2=26 list the numbers in the series: a1a2

a3a4a5a6

a7a8a9...

It can be seen that 6 numbers are in a cycle, and the number of 2006 6 is 2, so a2006=-6

3.To sell a module or add a sequence, as long as a(n+1) > a(n) will do.

So. 2n+1+λ>0

(2n+1)

2n+1) is up to -3, so >-3

The distance that Xiao Ming walked + the distance that Xiao Ming walked 27 = the distance that Dad walked, and the distance is equal to the distance of each step multiplied by the number of steps taken, and the number of steps taken is equal to the total time walked divided by the time required to walk each step.

According to the above, the equation can be 2a*c (5b)+27*2a=5a*c (8b).

If you get c b = 240, then the number of steps that dad runs is c 8b = 30

The key to solving the problem: When Dad chased Xiao Ming, Xiao Ming was still running, and the distance Xiao Ming ran = Dad's distance.

Suppose Dad needs to run at least x to catch up with Xiao Ming

27+x/5*8)/5*2=x

Let Dad need x steps to catch up with Xiao Ming, then Xiao Ming has taken a total of steps, and let Xiao Ming's distance per step be y, then the distance of Dad each step is, so the solution is x=30

That is, it takes 30 steps for Dad to catch up with Xiao Ming.

In total, you have to judge the truth or error of 47 20=940 questions.

If there is a total of x questions answered correctly, then there are (940-x) questions answered incorrectly.

The total score is 5x-(940-x) 1=6x-940=2(3x-470), and it is clear that the sum of the scores of the whole class is even.

Set 20 n questions to be correct, to get them wrong or not to answer them.

The fraction 5n (20 n) = 6n 20 is an even number.

From the title:

5 points for one and 1 point for the others;

Then, if you get the odd number question right, the score is odd number * 5 = odd number (a), and because there are 20 questions in total, the one who does not answer or answers incorrectly is also an odd number question, and the score that should be deducted is also an odd number (b) (odd number * 1 = odd number).

Therefore, the score of each student should be even (odd (a) - odd (b) = even), so the score of all students is also even. Even number * 47 = even number.

If you answer x correctly, you will answer (20-x) incorrectly, so the total score is: 5x-(20-x)=2(3x-10) Therefore, no matter how many questions you answer correctly, the score is even.

Even. All pairs are awarded 100 points each. Each person gets 95 points for 1 wrong question, minus 1 point for not answering or answering 1 question incorrectly, and deducting 1 point for even points.

90 points will be awarded for answering 2 questions incorrectly or not answering, and 2 points will be deducted for even points. Even points are minus even points for incorrect or not even questions, odd points are minus even points for incorrect or no odd questions, and even points are subtracted from odd points for incorrect or not answered odd questions, and even points are all in the end. Each person gets even points, and even numbers are multiplied by odd numbers to get even points, and finally even points are awarded.